Reading the sealed copy lower bound as an arithmetic lower bound

Exact statement

Reading the sealed copy lower bound as an arithmetic lower bound. Lemma R8.1 retains every original arithmetic gate once and permits only identity relays. Gate duplication, recomputation, equal-value sharing, different output SLPs, or a different bilinear algorithm can change the graph and invalidate the per-wire consumer count.

Statusrejected.

External reviewNo documented external or specialist review of the FPRD synthesis is recorded.

Context

The research record preserves failed approaches when they expose a model boundary, an invalid transfer, or an unsupported strengthening.

Proof or evidence

Lemma R8.1 retains every original arithmetic gate once and permits only identity relays. Gate duplication, recomputation, equal-value sharing, different output SLPs, or a different bilinear algorithm can change the graph and invalidate the per-wire consumer count.

Rejected transfers and surviving boundaries →

Verification notes

The failure status and preserved lesson are recorded in the cumulative failure ledger.

Limitations

state copy optimality only for sealed copy-only compilations of the fixed literal expanded DAG.

Open work

Keep this exclusion attached to any future reuse of the corresponding construction.